Finite Group Databasebeta

← #20256800

Subgroups — #20256800

Order 6016.

1160 conjugacy classes of subgroups; only the 471 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 471 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689722C216yesmaximal, complemented
2#15689713C216yesmaximal, complemented
3#15689685C213yesmaximal, complemented
4#15689659C216yesmaximal, complemented
5#15689636C216yesmaximal, complemented
6C2×(C22⋊D47)⋊C4C213yesmaximal, complemented
7C47×#543C211yesmaximal, characteristic, complemented
8C2×#10625354C2212yescomplemented
9C22×C22⋊D47C2213yes—
10C23×Dic47C2211yescharacteristic
11C22×C4×D47C2213yescomplemented
12#13094019C22112yescomplemented
13#13094015C2216yescomplemented
14#13094013C2216yescomplemented
15#13094009C22112yescomplemented
16#13094008C22112yescomplemented
17#13094000C2216yescomplemented
18#13093999C2216yescomplemented
19#13093998C2216yes—
20#13093998C2216yes—
21#13093994C22112yescomplemented
22Q8×Dic47C2212yescomplemented
23#13093986C2216yescomplemented
24(C22⋊D47)⋊C4C22112yescomplemented
25(C22⋊D47)⋊C4C22112yescomplemented
26#13093982C2216yescomplemented
27C2×Dic47⋊C4C2213yescomplemented
28C2×(C2×D47)⋊C4C2213yescomplemented
29C2×C4×Dic47C2213yescomplemented
30C22⋊Q8×C47C2216yescomplemented
31C22⋊Q8×C47C2216yescomplemented
32C2×C22⋊C4×C47C2213yes—
33C24×C47C2311yescharacteristic
34C23×D47C2313yes—
35C2×Q8×C47C2312yes—
36C2×Q8×C47C2312yes—
37C22×C4×C47C2313yes—
38C22×C4×C47C2313yes—
39C2×C22⋊D47—212no—
40C2×C22⋊D47C23112yes—
41C22×Dic47—42no—
42C22×Dic47C2313yes—
43C22×Dic47C2313yes—
44C22×Dic47C2313yes—
45#10625354—44no—
46C2×D188C2316yes—
47C2×D188C2316yes—
48C2×C4×D47—46no—
49C2×C4×D47C2316yes—
50C2×C4×D47C2316yes—
51C4⋊C4×C47C2316yes—
52C4⋊C4×C47C2316yes—
53C22⋊C4×C47C23112yes—
54(C2×D47)⋊C4C23112yes—
55(C2×D47)⋊C4C23112yes—
56(C2×D47)⋊C4C23112yes—
57C4⋊Dic47C2316yes—
58C4⋊Dic47C2316yes—
59Dic47⋊C4C23112yes—
60C4×Dic47C2316yes—
61C4×Dic47C2316yes—
62C23×C47—41no—
63C23×C47—41no—
64C23×C47#4114yescomplemented
65C23×C47C2413yes—
66C22×D47—26no—
67C22×D47—43no—
68C22×D47—43no—
69C22×D47C2416yes—
70Q8×C47—42no—
71Q8×C47—42no—
72C2×C4×C47—43no—
73C2×C4×C47—43no—
74C2×C4×C47C2416yes—
75C2×C4×C47C2416yes—
76C22⋊D47—224no—
77C2×Dic47—26no—
78C2×Dic47—26no—
79C2×Dic47—43no—
80C2×Dic47C2413yes—
81C2×Dic47C2416yes—
82C2×Dic47C2411yescharacteristic
83D188—46no—
84D188—46no—
85C4×D47—212no—
86C4×D47—46no—
87C22×C47—23no—
88C22×C47—23no—
89C22×C47—44no—
90C22×C47C2×#4116yes—
91C22×C47C2511yescharacteristic
92C2×D47—26no—
93C2×D47—26no—
94C2×D47—26no—
95C2×D47—412no—
96C4×C47—26no—
97C4×C47—26no—
98Dic47—26no—
99Dic47—23no—
100Dic47H(5,𝔽2)12yes—
101#3459—471nomaximal, Sylow
102C2×C47—26no—
103C2×C47C22×#4111yescharacteristic
104C2×C47C2×H(5,𝔽2)11yescharacteristic
105C2×C47#58511yescharacteristic
106D47—46no—
107#543D4711yescharacteristic, complemented
108#539—476no—
109#538—476no—
110#534—473no—
111#529—476no—
112#525—476no—
113C2×C4×D4—473no—
114C47#345911yescharacteristic, complemented, Sylow
115C2×#41—472no—
116C22×D4—473no—
117C23×C4—471no—
118C23×C4—473no—
119#126—4712no—
120#125—476no—
121#124—476no—
122#123—4712no—
123#123—4712no—
124C22⋊Q8—476no—
125C22⋊Q8C2×D4716yescomplemented
126C22⋊Q8C2×D4716yescomplemented
127#121—476no—
128#121—476no—
129#121—476no—
130#120—4712no—
131C4×Q8—472no—
132C4×D4—476no—
133C4×D4—4712no—
134C4×D4—4712no—
135#117—476no—
136C2×C4⋊C4—473no—
137C2×C22⋊C4—473no—
138C2×C22⋊C4C2×D4713yes—
139C2×C42—473no—
140C24—473no—
141C24C22×D4711yescharacteristic
142#41—1884no—
143C2×Q8C22×D4712yes—
144C2×Q8C22×D4712yes—
145C2×D4—4712no—
146C2×D4—476no—
147C2×D4—476no—
148C2×D4—9412no—
149C22×C4—473no—
150C22×C4—473no—
151C22×C4—473no—
152C22×C4—476no—
153C22×C4—476no—
154C22×C4—1886no—
155C22×C4—1882no—
156C22×C4C22×D4713yes—
157C22×C4C22×D4713yes—
158C4⋊C4—4712no—
159C4⋊C4—476no—
160C4⋊C4—476no—
161C4⋊C4C22×D4716yes—
162C4⋊C4C22×D4716yes—
163C22⋊C4—4712no—
164C22⋊C4—4712no—
165C22⋊C4—4712no—
166C22⋊C4C22×D47112yes—
167C42—476no—
168C42—476no—
169C23—41no—
170C23—41no—
171C23—476no—
172C23—946no—
173C23—1883no—
174C23—1883no—
175C23#1062535414yescomplemented
176C23C23×D4713yes—
177Q8—42no—
178Q8—42no—
179D4—9424no—
180D4—1886no—
181D4—1886no—
182C2×C4—43no—
183C2×C4—43no—
184C2×C4—471no—
185C2×C4—476no—
186C2×C4—473no—
187C2×C4—9412no—
188C2×C4—946no—
189C2×C4—946no—
190C2×C4—1886no—
191C2×C4—1883no—
192C2×C4C23×D4716yes—
193C2×C4C23×D4716yes—
194C22—23no—
195C22—23no—
196C22—44no—
197C22—946no—
198C22—946no—
199C22—946no—
200C22—18812no—
201C22C2×#1062535416yes—
202C22C24×D4711yescharacteristic
203C4—26no—
204C4—26no—
205C4—472no—
206C4—946no—
207C4—943no—
208C2—26no—
209C2—1886no—
210C2C22×#1062535411yescharacteristic
211C2H(5,𝔽2)×D4711yescharacteristic
212C2#1568995811yescharacteristic
subgroupG/H
center, FrattiniC22C24×D47
commutator, socleC22×C47C25
FittingC47×#543C2
hypercenter#543D47
hypocenterC47#3459
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #543

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #15689722C2semidirect
2. #15689713C2semidirect
3. #15689685C2semidirect
4. #15689659C2semidirect
5. #15689636C2semidirect
6. C2×(C22⋊D47)⋊C4C2semidirect
7. C47×#543C2semidirect
8. C2×#10625354C22semidirect
11. C22×C4×D47C22semidirect
12. #13094019C22semidirect
13. #13094015C22semidirect
14. #13094013C22semidirect
15. #13094009C22semidirect
16. #13094008C22semidirect
17. #13094000C22semidirect
18. #13093999C22semidirect
21. #13093994C22semidirect
22. Q8×Dic47C22semidirect
23. #13093986C22semidirect
24. (C22⋊D47)⋊C4C22semidirect
25. (C22⋊D47)⋊C4C22semidirect
26. #13093982C22semidirect
27. C2×Dic47⋊C4C22semidirect
28. C2×(C2×D47)⋊C4C22semidirect
29. C2×C4×Dic47C22semidirect
30. C22⋊Q8×C47C22semidirect
31. C22⋊Q8×C47C22semidirect
64. C23×C47#41semidirect
107. #543D47semidirect
114. C47#3459semidirect
125. C22⋊Q8C2×D47semidirect
126. C22⋊Q8C2×D47semidirect
175. C23#10625354semidirect